Secondary Fuzzy Clustering of Multi‐Dimensional 2D Time Series Arrays (SFC‐2DTSA) Using DTW Metric: An Application to Drought Data

In many industrial applications, such as healthcare, economics, and environmental science, unsupervised learning tasks are often associated with multivariate time series in multi‐dimensional datasets. This type of data has unique challenges and needs robust machine learning models. However, the existing literature has shown that the Euclidean distance‐based clustering techniques are ineffective. To this end, we propose two hybrid unsupervised learning models for secondary cluster analysis of multi‐dimensional multivariate time series datasets using multiple dendrograms of data matrices using fuzzy learning, traditional Dynamic Time Warping distance metric and its robust variant. A fuzzy least squares version is minimized with respect to ultrametric distance matrices and fuzzy membership degrees to obtain an optimal secondary fuzzy partition of the set of primary dendrograms. Furthermore, we also modify the previously proposed evaluation metric to assess new methods on real‐world data. Because the ground truth labels for the real‐world data are not available, particularly for the secondary partition, and the existing evaluation metric can only be used to measure similarity between exactly two dendrograms. The experimental results demonstrated the best performance of the new approaches compared to the existing Euclidean distance‐based approach on simulated and real‐world data.